Methods and apparatus for investigating earth formations

ABSTRACT

In accordance with illustrative embodiments of the present invention, an electrode array is utilized for investigating earth formations surrounding a mud filled borehole without undue influence from a conductive mud column. One manner of accomplishing this is to establish a potential distribution in the borehole as if the mud column were of the same resistivity as the formation. Alternatively, a zero potential gradient can be established at various regions in the mud column to effectively block current flow up or down the mud column.

limited Stat sun Schuster METHODS AND APPARATUS FOR INVESTIGATING EARTHFORMATXONS Mar. 19, 1974 2,872,637 2/1959 Blanchard 324/1 2,880,3893/1959 Ferre et a1. 3.262.050 7/1966 Threadgold et a1 324/10 PrimaryExaminerGerard R. Strecker Attorney, Agent, or Firm 5 7 ABSTRACT Inaccordance with illustrative embodiments of the present invention, anelectrode array is utilized for investigating earth formationssurrounding a mud filled borehole without undue influence from aconductive mud column. One manner of accomplishing this is to establisha potential distribution in the borehole as if the mud column were ofthe same resistivity as the formation. Alternatively, a zero potentialgradient can be established at various regions in the mud column toeffectively block current flow up or down the mud column.

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sum us 0F 10 PATENTED MAR I 9 I874 sum 08 HF 10 ELECTRON CKTS wkSukb33x5 um Nu METHODS AND APPARATUS FOR INVESTIGATHNG EARTH FORMATIONS Thisis a division of application Ser. No. 815,265, filed Apr. 7, 1969 nowabandoned.

This invention relates to methods and apparatus for investigating earthformations traversed by a borehole and more particularly toinvestigation of earth formations by so-called electrode typeinvestigating devices.

It is common practice to investigate earth formations traversed by aborehole with electrode type investigating devices to obtain a log ofthe electrical resistivity or conductivity of the formations versusdepth. One form of such an investigating device emits unfocused currentfrom one electrode and records variations in the potential differencebetween two other potential measuring electrodes. These potentialmeasuring electrodes can both be located near the current-emittingelectrode, both located at a relatively great distance therefrom, or onemeasuring electrode located near the currentemitting electrode and oneremotely located therefrom. The entire electrode array is continuouslymovable through a bore-hole so that variations in the measured potentialdifference can be recorded as a function of depth to provide indicationsof the resistivity or conductivity of the formations which formationsinclude the rock matrix and formation fluids. Examples of suchinvestigating devices are shown in U.S. Pat. No. 1,894,328 granted to C.Schlumberger on Jan. 17, 1933.

There are problems however which may arise when using theabove-described electrode type exploring devices under certain boreholeconditions. One such 'problem occurs when the mud fluid filling theborehole, i.e., the mud column, is much more conductive than theadjacent formations. In this event, the current emitted from theprincipal current-emitting electrode will tend to flow primarily withinthe fluid in the bore hole rather than within the formations. Thus, thepotential measuring electrodes would, in this case, tend to beinfluenced more by the conductivity of the mud column than that of theformations, thus introducing errors into the measurements.

Another class of electrode type logging devices acts to focus a beam ofso-called survey current" into the formations for the purpose of, amongother things, eliminating this borehole or mud column effect. In thisclass of exploring devices, a pair of focusing electrodes is located oneither side of a central survey current electrode. Current is emittedfrom all three electrodes, the current emitted from both focusingelectrodes being in-phase with the survey current emitted from thesurvey electrode so as to focus the survey current into a thin currentbeam which extends deeply into the formations. Typical examples of suchfocused electrode investigating devices are disclosed in U.S. Pat. Nos.2,712,627 granted to H. G. Doll on July 5, 1955 and 3,031,612 granted toM. F. Easterling on Apr. 24, 1962, However, as is typical with thesefocused electrode exploring devices, the radial investigation (i.e., theinvestigation in a direction perpendicular to the borehole axis) tendsto be relatively deep.

While both the focused and nonfocused exploring devices have heretoforeprovided good results, it would be desirable to have an additionalelectrode type exploring device which has a relatively shallow depth of'2 investigation, like the nonfocused exploring devices, but yet is notundesirably influenced by a conductive mud column.

Also, it is often desirable to obtain a measure of the resistivity information zones at different radii with respect to the borehole axis andto do so with only one run through the borehole. One such tool foraccomplishing this is the combination induction logging and focusedelectrode tool disclosed in U.S. Pat. No. 3,329,889 granted to D. R.Tanguy on July 4, 1967 which shows both coils and electrodes mounted onthe same mandrel. While the radial depth of investigation of the focusedelectrode tool shown in the Tanguy patent is relatively shallow, it isknown that an even shallower depth of investigation can be obtained withexploring devices which have most of the electrodes mounted on aborehole wall-engaging pad member. An example of this type of exploringdevice is disclosed in US. Pat. No. 3,379,965 granted to D. Tanguy etal. on Apr. 23, 1968. However, it is difficult to utilize such awall-engaging pad member simultaneously with an induction logging devicebecause of the adverse effect that the metal portion of the pad andconnecting arms have on the induction logging device.

Thus, it is an object of the present invention to provide an electrodetype exploring device which is compatible with an induction loggingdevice, yet has a radial depth of investigation comparable with a padmounted exploring device. Along the same lines, it is another object ofthis invention to provide an electrode type exploring device thatprovides both shallow and deep radial investigation at the same time.

While the focused type investigating devices discussed above are muchless sensitive to a relatively conductive mud column than the nonfocusedelectrode type devices, if the mud column is substantially moreconductive than the formation under investigation, the potentialdistribution produced by such a focused electrode device will tend to bealtered from the desired distribution thus giving rise to a possibilityfor error. in this connection, it is another object of the presentinvention to provide a focused electrode device of the type describedabove which would not be unduly affected by a highly conductive mudcolumn.

It is a further object of the present invention to provide new andimproved methods and apparatus for use with electrode type exploringdevices which substantially minimize the effect of a conductive mudcolumn on the measurement of resistivity or conductivity.

In accordance with the present invention, a method for investigatingearth formations penetrated by a borehole comprises moving a supportmeans carrying a plurality of electrodes through a fluid-filledborehole. Survey and auxiliary currents are supplied to at least one ofthe electrodes for emission into a media surrounding the support means,the emitted currents returning to at least one current return electrode.The potential distribution in at least a portion of a borehole ismeasured and at least one of the survey or auxiliary currents isadjusted to maintain a desired potential distribution in said portion ofthe borehole. By so doing, the survey current will tend to be forcedinto a formation to enable a measure of a formation characteristic to beobtained.

In one form of the invention, one of the currents is adjusted to give apotential distribution through a borehole which decreases as an inversefunction of distance.

This can be accomplished by controlling either the potential orpotential gradient at two or more points in a borehole.

In another form of the invention, the potential distribution at only onelocation in a borehole is controlled. In a desirable manner, thiscontrol takes the form of maintaining the difference in potentialbetween two points in a borehole at substantially zero volts so as toproduce a borehole interval of zero potential gradient. In arepresentative embodiment of this zero gradient form of the invention,survey and auxiliary currents are emitted from a centralcurrent-emitting electrode. The auxiliary current is returned to a pairof current return electrodes located on each side of the centralelectrode and the survey current is returned to another electrode. Thepotential distribution at location above and below the central andauxiliary current return electrodes is measured and utilized to adjustone of the survey or auxiliary currents until a desired potentialdistribution at these locations is established. By so doing, theauxiliary current will act to force the survey current out of theborehole and into the formations when the mud column is more conductivethan the adjoining formations.

Apparatus for practicing the invention and the methods thereof isillustrated in several embodiments.

The methods and apparatus of the present invention can find utility inmost any situation where a conductive medium surrounding or near theexploring device hampers the investigation of the formations adjoiningthe conductive medium. Thus, the present invention can find utility withexploring devices of the type where a plurality of electrodes aremounted on a borehole wall-engaging pad member so that the surveycurrent will be prevented from shorting through a conductive mudcake.Additionally, the present invention can be used in combination with theprior art focused electrode systems to prevent a conductive mud columnfrom having an adverse affect on the investigation operation.

In another form of the invention, reciprocal arrangements of theabove-mentioned embodiments can be used.

For a better understanding of the present invention, together with otherand further objects thereof, reference is had to the followingdescription taken in connection with the accompanying drawings, thescope of the invention being pointed out in the appended claims.

Referring to the drawings:

FIG. 1 shows a prior art nonfocused type electrode array in a boreholealong with a representation of equipotential lines and current flowwhich could be expected under certain conditions;

FIG. 2 shows the equipotential and current flow lines which could beexpected under adverse conditions with the FIG. 1 electrode array;

FIG. 3 is a plot of potential versus distance along the borehole axiswhen using an electrode type investigating system for various boreholeconditions;

FIG. 4 shows an electrode type exploring device in a borehole along withelectrical circuitry for energizing the electrodes in accordance withthe present invention;

FIG. 5 is a reproduction of one of the curves of FIG. 3 (correspondingto R R for purposes of explaining certain features of the presentinvention;

FIG. 6 shows an electrode type exploring device in a borehole inaccordance with another embodiment of the present invention;

FIG. 7 shows an exploring device in a borehole along withrepresentations of the adjoining formations for the purpose of definingcertain terms utilized in the explanation of the present invention;

FIG. 8 shows an electrode type exploring device in a borehole along withthe accompanying electrical circuitry in accordance with anotherembodiment of the present invention;

FIG. 9 illustrates typical current flow patterns which could be expectedfrom the investigating apparatus of FIG. 8;

FIG. 10 illustrates another embodiment of the present invention;

FIG. 11 illustrates the utilization of the present invention for thecase where a portion of the electrodes are mounted on a wall-engagingpad member;

FIGS. 12 and 1 3 illustrate various electrode arrays that could bemounted on the pad member of FIG. 11 for investigating the earthformations adjoining the borehole;

FIG. 13 illustrates the current flow pattern which could be expectedwith the FIGS. 12 and 14 electrode arrays;

FIG. 15 illustrates a prior art focused electrode type investigatingapparatus along with a typical plot of the equipotential lines andcurrent flow pattern produced by such an electrode array;

FIG. 16 illustrates apparatus for improving the prior art investigatingapparatus illustrated in FIG. 15 in accordance with the presentinvention; and

FIG. 17 illustrates how the apparatus of FIG. 8 can be modified toproduce a reciprocal arrangement thereof.

Referring now to FIG. 1, there is shown a prior art electrode arraysituated in a borehole 20 filled with a conductive drilling mud having aresistivity R for investigating an adjacent formation 21 having aresistivity R,. The electrodes comprise a currentemitting electrode Aand two potential measuring electrodes M and N. The current returnelectrode (not shown) is located at some considerable distance from theelectrodes A, M and N. In this FIG. 1 situation, the mud resistivity Ris considered to be substantially equal to the formation resistivity R,and thus the current flow (dotted lines) will be distributed evenly inall directions since the current return electrode is at electricalinfinity.

With the known current distribution, the equipotential lines 22 and 23passing through the measuring electrodes M and N can be drawnperpendicular to the current flow lines. In three dimensional space,these equipotential lines 22 and 23 will have the form of sphericalshells. By measuring the current emitted from the current-emittingelectrode A and the potential difference between the measure electrodesM and N, the resistivity of the shaded area of FIG. 1 can be determined.Thus, for example, assuming that the current emitted from electrode A isconstant, the difference in the potentials measured by the electrodes Mand N will vary in accordance with the resistivity of the shaded area ofFIG. 1 through the application of Ohms Law.

Now referring to FIG. 2, there are shown equipotential lines 24, 25, andcurrent flow lines (shown in dotted line form) when the mud resistivityR is substantially less than the formation resistivty Rf- In this FIG. 2case,

most of the current emitted from the electrode A will travel through thehigh conductivity borehole fluids and will not penetrate into theformation. Thus, knowing that the equipotential lines are perpendicularto the current flow lines, the equipotential lines 24 and 25 will takethe form shown in FIG. 2. Thus, in this extreme case, the difference inpotential between the measure electrodes M and N will be stronglyaffected by the value of the mud resistivity R,,,.

In FIG. 3, there is shown a plot of voltage potential versus distance Dalong the borehole axis for various ratios of the mud resistivity R tothe formation resistivity R,. If R,,, R,, the entire medium surroundingthe electrodes is one electrically homogeneous volume. In thishomogeneous case, the voltage potential V will decrease as an inversefunction of the distance D from the current source along the boreholeaxis (i.e., V M V /D), where V is the potential at the current sourceand )t is a constant characteristic of the current electrode A Thus, theR R; potential distribution curve of FIG. 3 corresponds to the sphericalequipotential relationship shown in FIG. 1. As the mud resistivitybecomes less than the formation resistivity, the potential versusdistance curve tends to flatten out as illustrated in FIG. 3. This is asexpected since the potential drop per unit distance through the boreholewhen the current flows through a highly conductive borehole or mudcolumn will tend to be small.

From the above, with the electrode systems of FIGS. 1 and 2, it can besaid that at any time the resistivity of the mud column is differentfrom the resistivity of the adjoining formations, the equipotentiallines will be different from the desired spherical distributionillustrated in FIG. 1. As is illustrated in FIG. 2, the resistivity ofthe mud column relative to that of the formation greatly affects theshape of the equipotential plot and thus greatly affects thedetermination of which portion of the formations and/or borehole isinvestigated. As was stated earlier, the prior art focused electrodeexploring devices tend to minimize this mud column effect, but at thesame time, tend to produce relatively deep radial investigation.

It is a purpose of the present invention to provide novel methods andapparatus for investigating resistivity or conductivity characteristicsof a formation regardless of the conductivity of the mud column. It isalso desired with the present invention to provide an exploring devicewith relatively shallow radial investigation characteristics which is,at the same time, relatively unaffected by a conductive mud column. Inone form of the present invention, this is accomplished by setting up apotential distribution through the borehole which will tend toapproximate the spherical equipotential distribution illustrated in FIG.1 regardless of the difference in resistivity between the mud column andformation. This is accomplished by enforcing a potential distributionthrough the borehole as if the resistivity R,, of the mud column wassubstantially equal to the resistivity R, of the formation. As discussedin connection with FIG. 3, this potential distribution curve for thehomogeneous case of R,,, R, is a potential curve which decreases as aninverse function of distance along the borehole axis. By enforcing thispotential distribution along the borehole axis, the potential shoulddecrease in the same fashion in the formation provided the formationitself is homogeneous.

Now turning to FIG. 4, there is shown apparatus for investigating theresistivity or conductivity of adjoining earth formations without beingunduly affected by the relative conductivity of the mud column. In theFIG. 4 apparatus, this is accomplished by controlling the potential attwo points in the borehole in accordance with the homogeneous condition(R,,, R,) curve of FIG. 3. More particularly, in FIG. 4, there is showna means for carrying a plurality of electrodes through a borehole 27filled with a conductive drilling mud for investigating adjoining earthformations 28. For purposes of explaining the operation of the FIG. 4apparatus, the forma tions 28 will be assumed to be homogeneous. In FIG.4, the carrying means includes a support means 33 which is suspended inthe borehole 27 on the end of an armored multic conductor cable 31 ofwhich the lower 109 feet or so is covered with a suitable insulatingmaterial 32. A remote potential measuring electrode N is mounted on thisinsulated portion of the cable 31 and is connected by a suitableelectrical conductor to electrical circuitry located in the supportmember 33.

The electrode array also includes a central currentemitting electrode Amounted on the support member 33 with a pair of symmetrical potentialmeasuring electrodes M and M, located equal distances d, from A on bothsides thereof. The electrodes M and M, are electrically shortedtogether. A second pair of potential measure electrodes M and M (alsoshorted together) are mounted on the support member 33 equal distances dfrom A on both sides there-of and at a greater distance therefrom thanthe first measure pair M,,M,'. A third set of electrodes (also shortedtogether) A and A, are mounted on the support member 33 at equaldistances on both sides of the center electrode A, and at greaterdistances therefrom than the aforementioned measure electrodes. Theexterior of the portion of support member 33 on which these electrodesare mounted is constructed of a nonconductive material. The upperportion 34 of the support member 33 is a fluid-tight housing whichcontains the electrical circuitry to which the aforemehtioned electrodesare connected.

Looking at the dotted line box 34a shown to the right of the borehole27, electrical circuitry contained within the fluid-tight housing 34 isillustrated. A constant current generator 35 supplies a constantmagnitude alternating current i between the central current-emittingelectrode A and the armor of cable 31. The potential difference eestablished between the measure electrodes M M, and the remote electrodeN is applied across the primary winding 36 of a transformer 37 and thepotential difference e, established between measure electrodes M ,M andremote electrode N is applied across the primary winding 38 of atransformer 39. The secondary windings 40 and 41 of transformers 37 and39 respectively are series connected and coupled to the input of a highgain amplifier 42.

The transformers 37 and 39 are wound in such a manner that the inputvoltage e; to amplifier 42 can be expressed as follows: m

where C is a constant. (C will be defined later.) The emplifier 42induces an output current ia in the secondary winding of a transformer43, which current is emitted from the central current-emitting electrodeA and returned to the two end electrodes A and A, for return to thesecondary winding of transformer 413.

The gain of amplifier 42 is sufficiently high that the input voltage 2thereto will be substantially zero volts. That is to say, amplifier 42will supply sufficient auxiliary current i between the centralcurrent-emitting electrode A and the end electrodes A A, to maintain theinput voltage e substantially equal to zero. Thus, setting e;, 0,Equation (1) can be rewritten as:

(2) Since the voltages e and e are measured with respect to the remotepotential reference electrode N, which because of its remoteness fromthe current-emitting electrodes, is at or substantially near zero volts,e and e will represent the potentials with respect to zero volts onmeasure electrodes M ,M and M ,M Thus, Equation (2) can be written as:

where V and V are the potentials with respect to zero volts'on measureelectrodes M M and M M respectively.

Now concerning the value of C and referring to FIG. 5, there is shownthe homogeneous potential distribution curve, i.e., the R,,, R, curve ofFIG. 3, reproduced. The location of the electrodes of FIG. 4 are shownalong the horizontal (distance) axis of FIG. 5. Since the potentialdecreases as an inverse function of distance from a current source in ahomogeneous medium, the potential V at the measuring electrode M, when RR, will be:

(4) where V is the voltage potential at the source. Likewise, thepotential V at the measuring electrode M will be:

VMI 2) 0 (5) Combining Equations (4) and (5), we have:

(m /VH (tn/d2) Thus, comparing Equations (3) and (6), it is clear thatthe circuit constant C (windings ratio of transformers 37 and 39) willbe equal to (d ld for the FIG. 4 apparatus to produce a potentialdistribution as if R were equal to R, regardless of the value of R,,relative to R,. In accordance with the operation of the feedback loop ofFIG. 4 just discussed, the auxiliary current i is continuously adjustedsuch that the potential Y is aly q a to d l ilyluin. ssqrs ansshEsiuatio (6). By so doing, a potential distribution curve will beproduced by the apparatus of FIG. 4 in substantially the form shown inFIG. 5. As discussed in connection with FIGS. 1, 2 and 3 a potentialdistribution curve of the shape shown in FIG. 5 represents the potentialdistribution fora homogeneous case, (i.e., R R Thus, by

enforcing this potential distribution in the borehole, a substantiallyspherical equipotential distribution similar to the one shown in FIG. 1will be established regardless of the conductivity of the mud columnrelative to the formation. This effectively has the result of making theformation and mud column appear to be one homogeneous medium and thusany adverse affect of the mud column on the investigation of theformation is substantially eliminated.

It would perhaps be beneficial to also discuss this operation in termsof current flow. In this regard, since the survey current emitted fromthe central currentemitting electrode A is returned to the relativelydistant cable armor 31 and the auxiliary current i is returned to thenearby electrodes A,,A,, the auxiliary current i will tend to passprimarily through the mud column thus forcing the survey current i outinto the formation for the investigation thereof. It is clear that themore conductive the mud column relative to the formation, the moreauxiliary current i will be generated to flow through the mud column inorder to insure that the potential relationship between the measuringelectrodes M and M is as set forth in Equation (6). If R,, is equal toR,, then there would be very little, if any, auxiliary current igenerated since the survey current i alone would set up the requiredpotential distribution for the same reasons as discussed in connectionwith FIG. 1.

Since the survey current i is always at a constant value (i.e., RMS orpeak-to-peak value) through the action of the constant current generator35, the potential existing on the central current-emitting electrode Awill vary in proportion to the resistivity of the media surrounding thiselectrode. In terms of the potential distribution curve of FIG. 5, theentire curve will move up or down in dependence on this resistivity. Toobtain a measure of the formation resistivity then, it is only necessaryto measure the potential difference between two points in the borehole.Thus, assuming that the difference between the potential in the vicinityof the measure pair M,,M, and the potential or remote electrode N ismeasured, that portion of a homogeneous formation lying between theequipotential line 45 which passes through the measure electrode pairM,,- M, and the equipotential line 46 which passes through the remotereference electrode N is investigated. Since the survey current returnelectrode (armor of cable 31) is remotely located relative to thecentral currentemitting electrode A and the potential distribution curveof FIG. 5 is established in the borehole, the survey current will tendto radiate from the central electrode A in a spherical fashion providedthe formation itself is homogeneous. Thus, the equipotential lines 45and 46 will be substantially spherical in shape as shown in FIG. 4. Byspacing the M ,M electrodes far enough from the central electrode A theborehole will be substantially eliminated from investigation since theequipotential line 45 passes through the formation.

A measurement of the resistivity of the formation lying between theequipotential lines 45 and 46 is obtained by coupling this potentialdifference between electrodes M M and N via a transformer 47 to asuitable high impedance input measuring amplifier 48. The output signalfrom measure amplifier 48 is supplied to the input of a phase-sensitivedetector 49 which derives its phase reference signal from the constantcurrent generator 35. The phase-sensitive detector 49 generates avarying DC output signal which is proportional to that portion of themeasured signal which is in-phase with the survey current and thus isproportional to formation resistivity R,

This resistivity signal is supplied to the surface of the earth via aconductor pair 50 (which in reality passes through the cable 31) to arecorder 51 via suitable signal processing circuits 52. The recorder 51is driven as a function of cable movement via a shaft 53 coupled to arotating wheel 54. The wheel 54 engages the cable 31 so as to rotate asa function of cable movement. By this means, the resistivity signal R,is recorded by recorder 51 as a function or borehole depth to produce alog of resistivity versus depth.

It is also possible to control the potential gradient at two points inthe borehole to produce the potential distribution curve of FIG. 5. Thepotential gradient is defined as (AV/AD) where AV is the difference inpotential between two fairly closely spaced points and AD is the spacingbetween these two points. Referring now to FIG. 6, there is shownapparatus for accomplishing this in accordance with the presentinvention. Like the FIG. 4 embodiment, the FIG. 6 embodiment includes aplurality of electrodes mounted on a support member 55. As in the FIG. 4embodiment, a central currentemitting electrode A is surrounded on boththe upper and lower sides thereof by a symmetrical electrode arraycomprising in the order of their spacings from the central electrode Athe electrodes M -M M.,M A,-A,', M M M -M and A A The M and M electrodesare spaced relatively close together and the center point therebetweenis a distance d, from the current source A The M and M electrodes arelikewise spaced relatively close together and the center pointtherebetween is a distance d, from the current source A(Correspondingly, the M M and M M are each spaced close together anddistances of d, and d from A respectively.) As in the FIG. 4 embodiment,similarly designated electrodes on both sides of the central electrode Aare shorted together.

The constant current generator 56 generates a constant magnitude ACsurvey current i which is emitted from the central current-emittingelectrode A and returns to the generator 56 via the armor of cable 31.The difference in potential AV between the potentials on the firstmeasure electrode pair M ,M and M ,M., is developed across the primarywinding 57 of a transformer 58 and the difference in potential AVdeveloped across the measure electrode pair M ,M and M ,M is supplied tothe primary winding 59 of a transformer 60. The secondary windings oftransformers 58 and 60 are series connected and coupled to the input ofa high gain amplifier 61. The windings of transformers 58 and 60 are setsuch that the input voltage e., to the monitor amplifier 61 is:

where C is a constant determined by the winding ratio of transformers 58and 60. The amplifier 61 develops an auxiliary current i in thesecondary winding of a transformer 62 which is emitted from the centralcurrent-emitting electrode A and returned to the auxiliary currentreturn electrodes A A and A and A A weighted current summing network 63sums the currents i and i which are received by the electrodes A ,A, andA ,A respectively for return to the secondary winding of transformer 62.These currents i and i are summed in a fixed ratio so that i ni Toaccomplish this, the i current passes through a resistor of value R andthe i current passes through a resistor of value nR,

where R is substantially higher than the resistance of the remainder ofthe feedback loop.

As in the FIG. 4 embodiment, the gain of amplifier 61 is sufficientlyhigh that enough auxiliary current i will be supplied between thecentral current-emitting electrode A and the return electrodes A -A A -Ato maintain the input voltage e., to amplifier 61 at substantially zerovolts. Thus setting e, 0, Equation (7) can be rewritten as:

( s-s/ sr) C2 To determine the constant C and turning to FIG. 5, thelocations of the electrodes M M M and M are represented as points on thepotential distribution curve. By taking the derivative of the earlierdiscussed potential distribution function V V /D), the slope of thepotential distribution curve at any point spaced a distance D from thecurrent source is:

and written for the potential gradient measured by the measuringelectrodes M ,M and M ,M is:

( l l Combining Equations l 6) and l l we have:

( s-a/ a-4) r l z (By making AD AD these terms drop out, although, ifthey were unequal, it would only change the constant portion (d ld ofEquation 12.) Comparing Equations (8) and (12), it is clear that thecircuit constant C should be equal to (dB/d to establish the desiredpotential distribution.

Thus, it can be seen that the FIG. 6 apparatus measures the potentialgradient at one location in the borehole by means of the measureelectrodes M and M and the potential gradient at a second location inthe borehole by means of the measuring electrodes M and M and adjuststhe auxiliary current i to maintain a constant ratio between thesepotential gradients. In other words, the ratio of the slopes of the FIG.5 curve at two borehole locations is maintained constant. By making thisconstant ratio equal to (dB/(If) a potential distribution curvesubstantially as shown in FIG. 5 will be produced by the FIG. 6apparatus and a spherical equipotential distribution will be establishedin the media surrounding the electrode array to thus eliminate the mudcolumn as a disrupting factor in the measurement of the resistivity orconductivity of the formations. The electrode spacings and the value ofn can be selected to produce the desired results. (Desirably, n can beselected to be approximately the same as the squared electrode spacingratio (d /d As with the FIG. 4 apparatus, the survey current i emittedfrom the central current-emitting electrode A of FIG. 6 is constant andthus the entire potential distribution curve'of'FlG. 5 will increase ordecrease as a function of resistivity. To provide a measure of theformation' resistivity, the potentials on the center taps of llllprimary windings 57 and 59 of transformers 58 and 60 are supplied to theinput ofa suitable measure amplifier 64. That component of the outputsignal from measure amplifier 64 that is in-phase with the surveycurrent i is detected by a phase-sensitive detector 65 which derives itsphase reference signal from the generator 56. The resulting detectedsignal is supplied to the surface of the earth as a varying DC signalproportional to the formation resistivity R,

Since the potentials supplied to the measure amplifier 64 are derivedfrom the center taps of the primary windings of transformers 58 and 60,the difference between the potentials existing midway between measureelectrodes M and M and the potential existing midway between measureelectrodes M and M is measured. For a homogeneous formation then, themeasured resistivity is representative of the resistivity of thatportion of the formation which lies between the spherically shapedequipotential line 66 which passes through a point midway between themeasure electrodes M and M and a point midway between the measureelectrodes M and M and the spherically shaped equipotential line 67which passes through a point midway between the measure electrodes M andM and a point midway between measure electrodes M and M This area isshown as the hatched line area in FIG. 6. It should be noted that, ifdesired, another measure circuit could be utilized to provide a measureof the formation lying beyond this hatched line area in FIG. 6 bymeasuring the potential difference between the center tap of eitherprimary winding 57 or 59 and the remote electrode N.

In the discussion up to this point, it has been assumed that theformation it self is relatively homogeneous, the only complicatingfactor being a highly conductive mud column. The apparatus of FIGS. 4and 6 each operates to substantially minimize the adverse effects ofthis conductive mud column on the formation resistivity measurements.However, as is many times the case, the formations are relativelynonhomogeneous. This non-homogeneity can take the form, for example, ofboundaries between the formation beds where one formation has aresisitivity substantially different from an adjoining formation.Additionally, in permeable formations, the drilling mud will invade theformation thus displacing all or a portion of the naturally occurringformation fluids contained in the invaded portion. In many cases, theresistivity of the invaded formation zone will be different from theresistivity of the noninvaded zone and sometimes the contrast will bequite large.

Referring to FIG. 7, there is shown a diagram of these various zones. Alogging tool 70 is shown in a borehole 71 immersed in a mud column witha resistivity R,,,. The invaded zone having a resistivity R is the zonenext adjacent to the borehole 71 and the noninvaded zone having aresistivity R, is that portion of the formation furthest removed fromthe borehole 71. The radius of invasion r, is the distance between thecenter of the borehole and the interface between the invaded andnoninvaded zones. In addition, nonhomogeneity occurs when formation bedshaving a resistivity R, different from the resistivity of the zonepresently under investigation are located adjacent the investigatedzone.

As discussed earlier, the apparatus illustrated in FIGS. 4 and 6 willset up a potential distribution curve illustrated in FIG. 5 along theborehole axis as well as radially into the formation. However, if theformation itself is not homogeneous, an exploring device attempting toestablish the potential distribution for a homogeneous formation will,in effect, be attempting to establish an unnatural potentialdistribution which may cause measurement errors, especially where theradius of invasion r,- is relatively shallow and the resistivitycontrast relatively high.

Thus referring to FIG. 8, there is shown another form of the presentinvention wherein the resistivity can be measured for substantially allformation conditions and yet the effect of a highly conductive mudcolumn on such measurements will be substantially minimized. This isaccomplished by maintaining a constant potential distribution in onlyone region on each side of the central current-emitting electrode. Inthis FIG. 8 embodiment, a support member is supported in the borehole onthe end of the cable 71. The support member 70 includes an electrodearray comprising a central current-emitting electrode A and a pluralityof symmetrically disposed electrodes on the upper and lower sides of thecentral A electrode. These symmetrical electrodes, in the order of theirspacings from the central electrode A are M M A,A M M and M M As in theprior embodiments, those electrodes having the similar designation(prime or no prime) are shorted together.

In FIG. 8, there is also shown a coil system or induction logging systemmounted on the support member 70. Only two illustrative coils 73 and 74are shown, which coils are embedded in a layer of rubber material (notshown) which encircle a center mandrel 75. The center mandrel 75 andcoils are enclosed by an outer sleeve member 76 of cylindrical shape.(Part of this sleeve member 76 is broken away in FIG. 8 for purposes ofshowing the coils located therebelow.)

Concerning the electrode construction, the A A and A, current electrodesindividually comprise a series of small rectangular metal plates whichare positioned to encircle the circumference of the sleeve member 76.The rectangular plates of each electrode are connected together by meansof a closed loop of slightly resistive wire which encircles the sleevemember 76 immediately below the rectangualr plates. The measuringelectrodes M M M M M and M on the other hand, are constructed in asimilar manner except that small metal discs or buttons are used inplace of the rectangular plates since these measuring electrodes do notemit or receive a large amount of current as do the current electrodes AA and A,'. This electrode construction could, of course, be used withany electrode system discussed herein and is not limited to just theFIG. 8 embodiment.

By utilizing the electrode construction shown in FIG. 8, the electrodesof the electrode array will not take the form of a closed conductiveloop and thus will have a negligible influence on the operation of theinduction logging system. In this manner, an electrode array and a coilarray can both be utilized simultaneously on the same support member.For a more detailed explanation of the construction of the coils andelectrodes of FIG. 8, see U.S. Pat. No. 3,329,889 granted to D. R.Tanguy on July 4, 1967.

Now concerning the electronic circuitry contained within the fluid-tighthousing 70, refer to the circuitry shown within the dotted line box 70a,which corresponds to the fluid-tight housing 70. An oscillator 78couples a constant reference voltage V across the secondary winding 79of a transformer 80. One side of the secondary winding 79 is connectedto the center tap of the primary winding 81 of a transformer 82. Themeasure electrodes M M 'are connected to one side of the primary winding81 and measure electrodes M M, are connected to the other side thereof.The other side of secondary winding 79 is connected to the measureelectrode M and M via the primary winding 83 of a transformer 84. Thesecondary winding of transformer 84 is coupled to the input of a highgain amplifier 85 which supplies sufficient auxiliary current i betweenthe control current-emitting electrode A and the current returnelectrodes A A, by way of a transformer 86 such as to maintain thepotential e across the primary winding 83 of transformer 84 atsubstantially zero volts.

The equation for the voltage e developed across the primary winding 83can be expressed as:

5 M, re[ VM1 2 where V is the voltage on the measuring electrodes M andM and V is the voltage existing on the center tap of primary winding 81of transformer 82, and thus the potential existing at a point betweenthe measuring electrodes M and M (and likewise M and M Since the actionof amplifier 85 supplying auxiliary current i, between the electrodes Aand A -A, maintains the voltage e developed across primary winding 83 atsubstantially zero volts, Equation (13) can be rewritten as:

Equation (14) states that this feedback circuit just described willoperate to maintain the potential difference between the measuringelectrodes M M and a point intermediate the measuring electrodes M M andM M at a constant reference level. This reference level is the constantreference voltage V developed across the secondary winding 79 oftransformer 80.

A signal proportional to the potential difference between the measureelectrodes M M and M M is supplied to an amplifier 87 by way of thetransformer 82 and the zero gradient contact of a double-throw switch180. Amplifier 87 supplies sufficient survey current between the centralcurrent-emitting electrode A and the outer metal sheath of thefluid-tight housing 70 via a transformer 88 to maintain a zero potentialdifference between the measure electrodes M,, M, and M2, M2.

To summarize the operation of that portion of the FIG. 8 apparatusdescribed thus far, refer to FIGS. 8 and 9 in conjunction where FIG. 9shows the current flow pattern produced by the apparatus of FIG. 8 in atypical situation. The amplifier 85 produces sufficient auxiliarycurrent i to maintain a constant potential difference between theequipotential line 94 which passes through the measuring electrodes Mand M and'the equipotential line 95 which passes through a point betweenthe measuring electrodes M,, M, and M M The amplifier 87, on the otherhand, supplies sufficient survey current i between the centralcurrentemitting electrode A and the outer metallic sheath of the housing77 to establish a substantially zero potential gradient (or zeroelectric field) between the measuring electrodes M M, and M M By sodoing, it is insured that no current will flow through the bore hole ina direction parallel to the borehole axis in the vicinity of themeasuring electrodes M M and M M By this means, the borehole will beelectrically plugged at the measuring electrodes M,, M, and M M the sameas if electrical insulators were placed in the borehole at these twolocations. This then prevents the survey current i from shorting throughthe borehole to produce the effect discussed in connection with FIG. 2.

Since the auxiliary current return electrodes are inside the electricalplugs (points of zero gradient) on both sides of the centralcurrent-emitting electrode A and the survey current return electrode(metal sheath 77) is outside the electrical plug, the auxiliary currenti will flow primarily in the borehole thus forcing the survey current iout of the borehole and into the formation, as shown in FIG. 9. Theauxiliary current i,, and survey current i will tend to break inopposite directions in the vicinity of the zero gradient locations withthe auxiliary current i being pulled back to the auxiliary returnelectrodes A and A and the survey current i tending to flow in theopposite direction away from the current electrodes A A and A,.

It should be noted here that even though the auxiliary current i is nolonger forcing the survey current i away from the conductivefluid-filled borehole at borehole locations above the measuringelectrodes M '--M and below the measuring electrodes M M the dimensionsof the borehole become important as the survey current moves further andfurther away from the central current-emitting electrode A Thus, eventhough the borehole may be far more conductive than the formation, asthe survey current moves further away from the A electrode, it will tendto spread out into the formation. By so doing, the volume of formationthrough which the survey current i passes becomes substantially greaterthan the volume of the mud column as the distance from the centralelectrode A increases and thus the overall resistance offered to thesurvey current by the formation becomes-less than the overall resistanceof the mud column. Thus, by appropriately placing the measuringelectrodes M M and M M the survey current will not have a tendency toreturn to the borehole at a distance away from the A electrode where theeffect of the auxiliary current has diminished.

The apparatus of FIG. 8 can produce a relatively shallow investigationof the formation. How shallow depends on the spacings between electrodesand the dimensions of the electrodes. This can be seen in flG. 9 byobserving that the auxiliary current i is constrained primarily to themud column and thus the survey current i does not have a tendency topenetrate deeply into the formation. This is contrasted with theso-called focused electrode" systems which force survey current deeplyinto a formation through the action of focusing current emitted fromnearby focusing electrodes, which focusing current is in-phase with thesurvey current. Electrode systems of this type can be found in US. Pat.No. 2,712,627 granted to H. G. Doll on July 5, 1955 or US. Pat. No.3,031,612 granted to M. F. Easterling on Apr. 24, 1962. It should benoted here that the potential on the auxiliary electrodes A and A, ofthe apparatus of the present invention is degrees out-of-phase with thepotential on the central current-emitting electrode A as compared withconventional focused electrode systems where the potentials of thesurvey and focusing electrodes are in-phase.

The radial depth of investigation of the apparatus of the presentinvention can be selected by properly selecting the placement and sizeof the electrodes. Thus, for example, by moving the measuring electrodesM M, and M M, of FIG. 8 closer to the central electrode A the radialdepth ofinvestigation becomes less. However, if moved too close, theborehole effect becomes a problem (i.e., much of the survey currentwould return through the borehole if it is conductive enough).Obviously, a compromise between the two conflicting considerations is inorder if shallow investigation is desired.

Additionally, the placement of the survey current return electrode issomewhat of a factor in determining the radial depth of investigation ifthis electrode is relatively close to A As shown'in FIG. 8, the currentreturn for the survey current i is the metal housing 77 which is locatedrelatively close to the current-emitting electrode A but exterior of themeasuring electrodes M,, M, and M M By so doing, the survey current i isprevented from penetrating too deeply into the formations. Recallingthat equipotential lines are perpendicular to current flow lines, theequipotential lines of FIG. 8 will no longer be spherically shaped sincethe survey current i is being drawn toward the housing 77. Thus, thedepth of investigation will tend to be relatively shallow as shown bythe equipotential lines 94 and 95 in FIG. 8. If desired however, thiscurrent return could be placed on the armor of the cable 71 as in theFIGS. 5 and 6 embodiments or these embodiments could have the i currentreturn electrode positioned as in the FIG. 8 embodiment.

After extensive research and experimentation, a desirable spacing of theelectrodes has been found to be: A to M and M and 4.4 inches; A to A andA and 8 inches; A to M and M, and 19 inches; A to M and M and 23 inches;and A to the housing 77 60 inches with the housing 77 extending upwardanother 2 feet or so.

Since the equipotential lines 94 and 95 of FIG. 8 have a constantpotential difference therebetween, it is clear that to obtain a measureof this hatched line portion of the formation shown in FIG. 8, it ismerely necessary to measure the survey current which passes therethroughto obtain a measure of the conductivity thereof. To accomplish this, avery low resistance measure resistor 89 is inserted in series with thesecondary winding 90 of transformer 88 so that a voltage proportional tothe magnitude of survey current i is developed across this resistor 89.This measure voltage is applied to a high input impedance measureamplifier 91 whose output signal is supplied to a phase-sensitivedetector 92. The phase-sensitive detector 92 detects that portion of themeasured voltage from measure amplifier 91 which is in-phase with theoscillator 78 output signal and provides a varying DC signalproportional to the conductivity 0-,, of the invaded zone (since theinvestigation is very shallow) to the surface of the earth.

It should be noted at this point that even though the survey current iwas generated in response to the potential difference between themeasure electrodes M,, M, and M M and the auxiliary current i,, wasgenerated in response to the potential difference between the M Mmeasuring electrodes and a point between the M M and M M electrodes,these two functions could be reversed. If this change were made, itwould be necessary to switch the return electrodes which are connectedto the secondary windings of transformers 86 and 88 so that the surveycurrent i will be returning from the housing 77 to the secondary windingof transformer 86 and the auxiliary current returning from theelectrodes A A, to the secondary winding of transformer 88. Measureresistor 89 would then be inserted in series with the secondary windingof transformer 86 to obtain a measure of the survey current.Additionally. even though a constant voltage system has been shown inFIG. 8 (which could be adapted to the FIGS. 4 and 6 embodiments aswell), a constant current system could just as easily be utilized.

It would be desirable at this point to briefly compare the form of theinvention depicted in FIG. 8 with that depicted in FIGS. 43 and 6. Theform of the invention illustrated in FIGS. 4 and 6 utilizes two pointsof control on each side of the central A electrode for maintaining apotential distribution substantially as shown in FIG. 5. Thus, the FIG.4 apparatus maintains a constant ratio of the potentials measured byelectrodes M M and M M while the apparatus of FIG. 6 maintains aconstant ratio of the potential gradients at the electrode pairs M M M Mand M M M M to achieve the potential distribution curve of FIG. 5. Theform of the invention shown in FIG. 8, on the other hand, only utilizesone point of control on each side of the central A electrode, namely, azero potential gradient at the measuring electrodes M M and M M By sodoing, the borehole is electrically plugged thus forming the surveycurrent to flow outwardly into the formation and not short through theborehole.

Thus, in a homogeneous formation, a potential distribution curvesomewhat similar to that shown in FIG. 5 will be produced by the FIG. 8apparatus in much the same manner as in the FIGS. 4 and 6 apparatus.However, when the formation is relatively nonhomogeneous, the FIGS. 4and 6 apparatus will attempt to es tablish the homogeneous case or typepotential distribution in this nonhomogeneous formation which may tendto produce errors in the measurements while the FIG. 8 apparatus willallow the potential distribution in the formation to take its naturalcourse, but without undue influence from the mud column.

It will be recalled from a discussion of FIG. 5 that to produce aspherical equipotential distribution in a homogeneous formation, thepotential distribution depicted in FIG. 5 must be established in theformation. However, since the system of FIG. 8 establishes a region ofzero potential gradient on both sides of the central A electrode, it canbe seen that even if R,, R; and the formation itself is homogeneous, theFIG. 8 apparatus will not establish a spherical equipotentialdistribution. However, if the monitoring electrodes M M,-M M are locatedat a sufficient distance from the central survey electrode A thepotential distribution will be so near spherical that the simplicity ofthe electronic circuitry is worth the slight error. (Note: This errorcan be corrected for by suitable correction charts.) The reason for thissimplicity is that is is easier to maintain a zero potential gradientthan a finite value thereof.

If however, an exact spherical distribution were considered desirablefor the homogeneous formation case, the FIG. 8 circuitry could bemodified to bring this about by establishing a finite potential gradientat the monitoring electrodes M M M M This could be accomplished, forexample, by adding a constant reference amplitude signal derived fromthe oscillator 78 by way of another secondary winding 79a of thetransformer 80 with the voltage developed across the secondary winding82a of transformer 82. Thus, in FIG. 8, the switch 180 would bepositioned in the finite gradient position so that the i amplifier 87will cause sufficient survey current to be emitted from the A electrodeto maintain V equal to the reference voltage developed across thesecondary winding 79a. The value of this gradient can be set by suitablyselecting the number of turns for secondary winding 79a. Desirably, thisgradient should be maintained at a value which will maintain a sphericalequipotential distribution in a homogeneous formation. Thus, referringto FIG. 5, if the measuring electrodes M M, and M M are at the locationsdesignated 184 and 185, the reference voltage developed across thesecondary winding 79a would be set at a value to produce a gradientdefined by the slope of the curve at the region defined by the points184 and 185.

In this alternative FIG. 8 case, the current flow through the boreholewould be regulated to a desired degree thus preventing very much of thesurvey current from shorting through a conductive mud column. Thus, in ahomogeneous formation, the amount of current allowed to pass through theborehole would be no greater than the current flow in any otherdirection thus establishing the spherical equipotential situation ofFIG. 1. However, if the formation is nonhomogeneous, the potentialdistribution in the formation can take any form since the potentialdistribution for a homogeneous formation will not be enforced along thelength of the electrode array. Effectively, then, in this modifiedversion of FIG. 8, the borehole is electrically plugged at the measuringmeasuring electrodes M M, and M M except for a small flow of surveycurrent.

It should be noted at this point that even though the FIG. 8 apparatusmaintains a constant potential difference between two points along theelectrode array and the FIGS. land 6 apparatus maintain a constantsurvey current flow, these controls cannot be classed as controlsnecessary for performing the objects of the present invention. Instead.these constant voltage and constant current controls are merely controlsof convenience rather than necessity. That is to say, by maintainingeither the voltage or current constant, it is only necesary to measurethe other variable electrical parameter to obtain a measure of eitherthe resistivity or conductivity of the formation. The FIGS. 4, 6 and 8apparatus would work just as well if neither the voltage nor currentwere maintained constant and the variations in both parameters measuredso that a ratio of voltage to current would produce a resistivitymeasurement. Moreover, in the FIGS. 4, 6 and 8 embodiments, either the ior i current could be utilized to control the potential distribution.

It should also be noted that the equipotential plots discussed earlier,as well as those to be discussed later, are estimates of the realsituation since it is impossible to measure them point by point in theformation. Also, these equipotential plots are drawn for homogeneousformations and will tend to become somewhat distorted in nonhomogeneousformations.

As set forth above, it is only necessary to have one region of controlon each side of the central A electrode and one control parameter toproduce the desired results in accordance with the present invention.However, if desired, there could be a plurality of zero (or finite)potential gradient control regions to achieve the objects of the presentinvention. Thus, referring to FIG. 10, there is shown a more elaborateembodiment of the present invention utilizing the technique set forth inFIG. 8. As in the prior embodiments, the central current-emittingelectrode A is surrounded on both the upper and lower sides by asymmetrical electrode array comprising in the order of their distancefrom the central electride A the electrodes M 0; A1, A1,; M1, l 21 M2,;A2, A2; A3, A3,; M3, M3, and M M The M,, M, and M M measuring electrodesare located relatively close together as are the measuring electrodes MM and M M As before, the upper portion of the support member 102comprises a fluid-tight housing 103 containing the electrical circuitry.

This electrical circuitry is shown in the dotted line box 103a in FIG.10 and includes a constant current generator 104 which supplies aconstant value of survey current i between the central current-emittingelectrode A and the armor of the cable 31. A high gain amplifier 105 isresponsive to the potential gradient between the measuring electrodesM,, M, and M M via a transformer 106 for supplying sufficient auxiliarycurrent i between the central current-emitting electrode A and thecurrent return electrode A A via a transformer 107. As before, themagnitude of this auxiliary current i is sufficient to maintain thepotential gradient between the measuring electrodes M M, and M M atsubstantially zero volts. This operation is the same as in the FIG. 8embodiment. However, in this FIG. 10 embodiment, another high gainamplifier 108 is responsive to the potential gradient between themeasuring electrodes M M and M M via a transformer 109 to supplysufficient auxiliary current i g between the current electrodes A A andA A so as to maintain the potential gradient between the measuringelectrodes M M and M M at substantially zero volts. Thus, it can be seenthat the apparatus of FIG. 10 operates to plug the borehole at twoseparate points on each side of the central current-emitting electrode ABy this means, the survey current I emitted from the central electrodeA, will be forced out of the borehole into the formation for a greaterinterval than would be possible with the FIG. 8 apparatus. This could beadvantageous for example if the mud column were so much more conductivethan the formation that a great amount of the survey current i wouldtend to be drawn into the mud column at a point just beyond the firstmeasuring electrodes M M and M M. Additionally, it has been found thatthe radial depth of investigation will be slightly decreased if thissecond loop is utilized.

To obtain a measure of the resistivity of the adjoining formations withthe FIG. 10 apparatus, a number of possibilities exist. For example, thepotential difference between the measuring electrodes M M and a pointintermediate of the first measuring electrode pairs M,, M, and M M couldbe measured. Likewise, the potential existing at a point between thesecond measuring pairs M M and M.,, M, or the potential of the remoteelectrode N could be utilized in some combination with the M or M -Mpotentials. In FIG. 10, there is shown apparatus for measuring thedifference be-

1. Apparatus for measuring a characteristic of earth formationstraversed by a borehole, comprising: a plurality of electrodes; meansfor mounting said electrodes for passage through a borehole; means forsupplying a first current to a first one of said electrodes for emissioninto the media surrounding the mounting means, said first currentreturning to a relatively remote electrode for return to the currentsupplying means; means responsive to the potential difference measuredbetween two points in said borehole for supplying a second currentbetween said first electrode and an electrode relatively near said firstelectrode of sufficient magnitude to maintain said potential differencein a substantially fixed relationship; means responsive to the potentialdifference between two points in said borehole located a first distanceapart for obtaining a measure of a characteristic of a first portion ofsaid formation; and means responsive to the potential difference betweentwo points in said borehole located a second distance apart forobtaining a measure of the characteristic of a second portion of saidformation, said second formation portion being then different from saidfirst formation portion.
 2. Apparatus for measuring a characteristic ofearth formations traversed by a borehole, comprising: a plurality ofelectrodes including at least one current-emitting electrode, a pair ofmeasuring electrodes located above said at least one current-emittingelectrode and a second measuring electrode pair located below said onecurrent-emitting electrode, a current return electrode pair having oneelectrode each located between said at least one current-emittingelectrode and each of said measuring electrode pairs, and a thirdcurrent return electrode spaced apart from said other electrodes; meansfor mounting said electrodes for passage through a borehole; means forsupplying a first current to said at least one current-emittingelectrode for emission into the media surrounding said mounting means,said first current returning to said third current return electrode forreturn to the current supplying means; means responsive to the potentialdifference between at least one of said pairs of measuring electrodesfor supplying a second current between said at least onecurrent-emitting electrode and one of said return electrode pairs orsaid third return electrode to maintain a given relationship between thepotentials of said measuring electrodes; means responsive to thepotential difference between two points in said borehole located a firstdistance apart for obtaining a measure of characteristic of a firstportion of said formation; and means responsive to the potentialdifference measured between two points in said borehole located a seconddistance apart for obtaining a measure of a characteristic of a secondportion of said formation which is different from said first formationportion.
 3. A method of measuring a characteristic of earth formationstraversed by a borehole, comprising: moving a plurality of electrodesthrough said borehole; supplying survey current between at least onecurrent-emitting electrode and a first return electrode; measuring thepotential distribution at borehole locations on opposite sides of saidat least one current-emitting electrode; supplying auxiliary currentbetween said at least one current-emitting electrode and two otherelectrodes of which one each is located between said at least onecurrent-emitting electrode and each of said potential monitoringlocations in response to measured potential distribution; measuring thepotential difference between at least two points spaced a first distanceapart in said borehole to obtain an indication of a characteristic of afirst portion of said formation; and measuring the potential differencebetween at least two other points spaced a second distance apart in saidborehole to obtain an indication of a characteristic of a second portionof said formation, said second formation portion being different fromsaid first formation portion.
 4. A method of measuring a characteristicof earth formations traversed by a borehole, comprising: moving aplurality of electrOdes through said borehole, said electrodes includingat least one current-emitting electrode, a pair of measuring electrodeslocated above said at least one current-emitting electrode and a secondmeasuring electrode located below said one current-emitting electrode, acurrent return electrode pair having one electrode each located betweensaid at least one current-emitting electrode and each of said measuringelectrode pairs, and a third current return electrode spaced apart fromsaid other electrodes; supplying a first current to said at least onecurrent-emitting electrode for emission into the media surrounding saidborehole, said first current returning to said third current returnelectrode; supplying a second current between said at least onecurrent-emitting electrode and one of said return electrode pairs orsaid third return electrode in response to the potential differencebetween at least one of said pairs of measuring electrodes to maintain agiven relationship between the potentials of said measuring electrodes;providing a measure of a characteristic of a first portion of saidformation in response to the potential difference between two points insaid borehole located a first distance apart; providing a measure of acharacteristic of a second portion of said formation in response to thepotential difference between two points in said borehole located asecond distance apart, said second portion being different from saidfirst portion of said formation.